This disclosure relates to geomechanical modeling, and, in particular, relates to use dynamic boundary conditions from time-lapse seismic data to update or refine the geomechanical model.
Geomechanical modelling of the subsurface can be used to study the stresses and strains introduced by injection and production. A proper understanding of the stresses and strains is necessary to avoid drilling hazards, maximize recovery and ensure reservoir integrity.
Time-lapse seismic data may provide information about the dynamic behavior of the subsurface between two seismic surveys, including density and velocity change and displacement of seismic events. Inversion may be used to relate the time-lapse changes to changes in rock properties, pressure, temperature, saturation and rock displacements.
Changes in the subsurface imply modified stresses and strains in and around the location where the changes occur. In the geomechanical simulation model, the modified stress and strain state is typically governed by a stress increment or a displacement increment applied to the model. Stress increments may be derived from changes in pressure, temperature and saturation, whereas displacement increments derived from time-lapse seismic data have not been studied widely.
Estimates of actual rock displacements from time-lapse seismic displacements rely on estimates of the velocity of the rock and how rock displacements modify the velocity. A commonly used approximation of the relationship between relative velocity change and actual rock strain is the R factor (Hatchell and Bourne, 2005a, 2005b), defined by
            δ      ⁢                          ⁢      v        v    =            -      R        ⁢                  ⁢                  ɛ        zz            .      Here δv/v is the relative velocity change, while εzz is the vertical strain. Assuming that the changes are small, the relative change in two-way travel time, referred to as the time strain, can then be expressed as
            d              d        ⁢                                  ⁢        t              ⁢          (              δ        ⁢                                  ⁢        t            )        =            2      ⁢              (                              ɛ            zz                    -                                    δ              ⁢                                                          ⁢              v                        v                          )              =                  (                  1          +          R                )            ⁢                        ɛ          zz                .            
The two-way travel time shift measured from time-lapse seismic data is an effect of accumulated time strain. An estimate of the R factor is required to convert the two-way travel time shift to an estimate of the actual rock displacement.
An important goal of geomechanical modeling is to use the mismatch between simulation results and time-lapse observations to update the material properties, the fault/fracture model and/or the model of the rock strain-velocity change relationship. A properly calibrated geomechanical model can be used for predictions. In addition, results from geomechanical modeling may help in interpreting time-lapse data.